Here's the weird thing about this storied rivalry between two programs that have long ruled the ACC like a shared fiefdom: Duke and North Carolina are always very good, of course, but, with the possible exception of 2004-05, they're rarely dominant at the same time.

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OK, so this might not be a typical Duke-North Carolina season. After all, neither is a No. 1 seed right now. (And that's pretty rare, based on history.) Joe Lunardi takes a look at the last month and what it might mean for each come Selection Sunday.

Making plans for the Final Four? Sure your team has all the pieces to make a run? Well, we have some bad news. Here's what's going to keep each contender from reaching college basketball's final weekend.

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It's almost as if they take turns.

See for yourself. Here's how I'd rank the 10 best teams these storied programs have produced, starting when Roy Williams took the job in Chapel Hill in 2003.

(Yes, the 2017-18 Blue Devils and Tar Heels were eligible for inclusion here. No, neither one made the cut.)

You'll note the presence of 10 different seasons, with zero instances where both teams were list-worthy in the same one. Go figure.

More to the point, Duke and North Carolina have produced an amazing number of historically great teams over the past 15 seasons. Enjoy.

JJ Redick was a Duke staple during the mid-2000s. AP Photo/Bill Kostroun, File

By the end of the 2015 NCAA tournament, this Duke bunch was a fit opponent for any team on this list -- but it wasn't always pretty getting to that point. The Blue Devils gave up a whopping 177 points in back-to-back January losses to NC State and Miami. One-and-done freshmen just can't play defense, it was said. Then Mike Krzyzewski's one-and-done freshmen -- Okafor, Winslow and Tyus Jones -- started playing defense, aided and abetted by old geezers Cook and, especially, Amile Jefferson. The rest is history: Duke went 21-2 after its January defensive holiday, and Okafor set a standard worthy of a latter-day Bagley or Ayton for simultaneous 2-point sorcery and tireless hegemony on the offensive glass. To win a national title in a season where one of the strongest Final Fours of the tournament's modern era had self-assembled is no small claim to fame. The Blue Devils of 2015 can always make that boast.

This might be a surprising choice at No. 2, but who among us is to say what is right and what is wrong? I am. I'm right. It's not this team's fault that it never got (and still doesn't get) the respect it deserved. The proof is in the performance. Duke fans today would collapse in a dazed collective stupor if they saw a few possessions of shutdown defense like those played consistently by this team. Meanwhile, on offense, Zoubek ruled the offensive boards like a ruthless despot on the rare occasions when 3s from Scheyer, Singler and Smith didn't fall. No, this team didn't put a single player into the first or even second round of the 2010 professional draft. Well, NBA, schmem-BA. Duke that season was statistically elite, not to mention a demographic precursor to the likes of Villanova 2016 and, possibly (we'll have to wait and see), the best teams of 2018.

Everything was set in the bracket that season, and everyone just knew that Duke and Connecticut would meet on the first Monday in April to decide the national title. Neither team made it that far, of course, but UConn's demise at the hands of George Mason has at least been observed ever since as a classic of the upset genre. The Blue Devils' exit that March was less iconic but no less jarring. Coach K's team was manhandled by Glen Davis and, especially, Tyrus Thomas of LSU, as Redick was pitilessly hounded into a 3-of-18 self-immolation from the field.

Up until the closing minutes of the national semifinal against Emeka Okafor and Connecticut, Redick and Deng had powered the Blue Devils to one of the better seasons posted by a program famous for recording highly successful seasons. Then the Huskies closed the game by scoring 12 straight points against a thinned Duke rotation (Williams, Shavlik Randolph and Nick Horvath all fouled out) and capturing the win, 79-78. UConn's triumph came against a team that to this day stands out as having one of the better combinations of elite offense and dominant defense that you'll run across.

With the exception of losses in four true road games, the defending champions were up to the task all season long, including a dominant three-game march to a title at that year's ACC tournament. That sheen of invulnerability suffered a hit, however, when No. 8 seed Michigan took Singler, Smith and Curry to the closing seconds of the game before the Blue Devils prevailed in the round of 32. The close shave against the Wolverines turned out to be prophetic. In the Sweet 16, Derrick Williams led No. 5 seed Arizona to a 55-point second-half explosion that ended Duke's season.

Joel Berry II and the Tar Heels won a national title a year ago. Jeremy Brevard-USA TODAY Sports

This title was the culmination of the strongest three-season run that either of these programs has recorded in the past 15 years: Hansbrough, Lawson and Ellington finally closed the deal in 2009. Few national champions in the tournament's modern era have ever imparted a sense of inevitability quite like the Tar Heels did that March. No tournament opponent came closer than 12 points to the Tar Heels at the final horn, and, famously, the national title game against Michigan State was effectively over by halftime. (The AP write-up of a game UNC won 89-72 pointed out correctly that "it wasn't that close.") Hansbrough received a decent amount of publicity (it's true!), but it was Lawson who put together what still stands as possibly the Platonic ideal of a season for a scoring point guard and who, to the everlasting credit of the voters, took home ACC player of the year honors.

I'll go out on a limb and say this was the best UNC-Duke team of the era to not win the national title, but I'll grant that the competition for that label is fierce. We might never know what got into the Tar Heels -- or, perhaps, what got into Kansas -- in the first half of that fateful national semifinal against the Jayhawks, but, until that 20-minute sequence it was surpassingly easy to envision everything falling into place for this team. UNC was, of course, the tournament's overall No. 1 seed, and Williams' team had been ranked No. 1 in the nation in 14 of that season's 20 AP polls -- including the first and the last ones. Indeed, in some ways (such as offensive rebounding), Hansbrough, Lawson and Ellington were actually superior to what they'd be in one year's time when they did win it all. Alas, the hoops gods said no.

The 2005 national champions were above all else a complete team. True, in keeping with Roy Williams' stylistic preferences, the Tar Heels didn't attempt many 3s. That being said, McCants, Felton and Jawad Williams shot a combined 42 percent from beyond the arc that season. May was an unstoppable force on the offensive glass (and also provided highly effective if rather underrated rim defense), and the UNC roster that season was so ostentatiously loaded that 2005 No. 2 overall NBA pick Marvin Williams came in off the bench.

By 2017, Roy Williams had mastered the art of generating (way) more shots than the opponent. His teams had always been magnificent on the offensive glass, of course, but, by the time you get the UNC team that reached two consecutive national title games, you're looking at the lowest turnover rates of Williams' tenure. That, plus Jackson setting a school record for made 3s, was more than enough for Meeks, Hicks, Berry & Co. to win it all one year later than it was "supposed" to happen (back when Brice Johnson and Marcus Paige were still around).

If not for a classic Kris Jenkins game winner for Villanova, we might be looking at back-to-back national titles for UNC. (Repeat, might. Jenkins' shot came with the score tied. A miss there meant OT, not an instant title for the Heels.) North Carolina enjoyed a notably smooth run to the title game (far smoother than many of these same players would record one year later), and the unparalleled inside-outside combination formed by Johnson and Paige seemed poised to bring home a banner. They very nearly did.

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